I not only have seen spectrographs of the atmospheric radiative effect, I actually own a copy of Grant Petty's book A First Course in Atmospheric Radiation", and have taught both undergrad and grad electrodynamics for over 30 years. Precisely what does this have to do with my statements above? I'm not "denying" that the greenhouse effect exists -- there is direct spectroscopic evidence for it. I can derive one simple model (a complete absorber model leading to 1.19x warming) for it on a piece of paper in three minutes. I regularly argue with people who want to claim that it doesn't exist at all, or that it violates the second law. Both are absurd -- of course it exists, and no it doesn't violate the laws of thermodynamics it is a direct consequence of them (although the actual atmospheric radiation effect is a great deal more complex than simple single layer models!)

All of this is completely irrelevant to my statements above. Let me explain the null hypothesis, since the terminology apparently eludes you. It is this: Supposed we increase atmospheric CO_2 from 300 to 600 ppm in the very simplest model planet we can imagine -- one where the *only* change we permit is this. One can work through the arguments for the greenhouse warming one should expect -- they involve looking at the measured spectrum of CO_2, doing a bit of work with the relevant Beers-Lambert formula, and thinking a bit about the lapse rate -- but in the end most people who do the calculation end up with somewhere between a 1 C and 1.5 C warming.

At this point one invokes the principle of ignorance -- *we don't really know* how the *entire Earth system* will respond nonlinearly to this. Nor do we have any plausible means with which to measure it -- we have no experimental Earths to do controlled observations with similar structure, e.g. 70% saltwater ocean confined in a complex pattern of continents -- and we already know that the establishment of *particular* circulation patterns of the confined ocean and atmosphere were the sole really plausible explanation for the Pliestocene ice age, which started when the isthmus of Panama closed between 3 and 4 million years ago.

We also know one important point from *linear* stability analysis. For the Earth's climate system to be stable *at all*, it has to respond to perturbations in forcing by *opposing the change*, not augmenting it. That is, at a stable point, the response to all perturbations has to be to push the system back *to* the stable point, not away from it, or the point isn't stable, it is unstable, like balancing a pencil on its point. This principle is taught in introductory first year physics, so presumably you are familiar with it.

The Earth's top of atmosphere "forcing" varies by roughly 90 W/m^2 every year, simply from the eccentricity of the Earth's orbit. It varies by order of a percent from fluctuations in albedo (mostly due to clouds, but also due to shrinking and expanding ice and snow fields) on a much shorter time scale, as short as days. The climate is if anything remarkably stable, at least on a short time scale (and we have the devil's own time explaining *any* of the longer time scale variations observed in the paleo record or the much shorter thermometric record, where the stable point itself exhibits considerable climate "drift" even while remaining sufficiently locally stable to be still considered "climate"). There is little evidence of any sort of runaway nonlinear instability from this natural variation in forcing. Quite the opposite, in fact, right up to the point where factors we *do not yet really understand and cannot compute or predict* seem to cause transitions like the advent of glaciation in the current, continuing, Pleistocene ice age.

Given a lack of knowledge of how the enormously complex system will respond to a small, linear variation in forcing on top of the annual *periodic* variation in forcing that is roughly *two orders of magnitude larger* and incidentally is in *counterphase* with the annual associated variation in global average temperature (just so you can see how non-intuitive and complex the Earth as a planetary climate really is), the null hypothesis is that it will simply shift the equilibrium, linearly, by the base estimate above. That is, doubling CO_2 will *most likely* increase the planet's mean temperature by roughly 1.25 C, call it 2 whole degrees F. This is of the same order as the temperature change associated with the Little Ice Age (descent into, emergence from) or the natural variation in global temperature that has been proceeding over the entire Holocene interglacial. It is unlikely to be catastrophic. It isn't even out of proportion to the warming we might have observed without the help of CO_2, or the warming we *did* observe over the first 2/3 of the thermometric record where CO_2 was an irrelevant factor.

This null hypothesis -- that the warming we should most likely expect due to doubling CO_2 is the direct warming from the CO_2 itself neither augmented nor diminished by nonlinear feedbacks we cannot compute, justify, or directly observe however much people do love to *argue* about them -- is the assertion that has to be *disproved* by temperature observations over -- according to all the climate people themselves: time spans in excess of (say) 25 years. Most climate people also seem to agree that CO_2 was an ignorable factor in climate forcing before the post-WWII industrialization (in particular that it was irrelevant to the substantial warming that occurred in the *first* half of the 20th century, even though that is all rolled into one convenient "hockey stick" in presentations without ever acknowledging that subtle point. So, start at 1940 (to avoid picking any "particular" start date, you can look at any date "around" 1950) and what do we see:

http://www.woodfortrees.org/pl...

There is one single visible episode of warming in this entire record. It is confined to a stretch of time that *is not as long* as 25 years -- it is pointless to try to pick endpoints of linear trends in this obviously nonlinear trended timeseries but the *eye* can clearly see that the warming is pretty much confined to the stretch between a start somewhere 1975 and 1985 and an end somewhere between 1995 and 2000. If one uses the most optimistic set of assumptions possible, this stretch is a "climate shift" across 1975 to 2000 to barely make 25 years. But this really is cherrypicking in the extreme, especially when the big bumps at the beginning and end can be tied to discrete *non*-driven-climate events -- ENSO, and the warming stretch itself coincides with the warming phase of the Pacific Decadal Oscillation and hence some fraction of it is probably natural.

So the big question is, does this graph falsify the null hypothesis, that the observed warming over the entire stretch of ~65 years is due to some mix of unknown, and really uncomputable, natural variation due to all of the internal coupled feedbacks that otherwise conspire to leave the system pretty stable (except when it isn't) plus the linear forcing due to CO_2 only?

Well, the warming observed is somewhere between 0.4 and 0.5 C over (say) 65 years as CO_2 has gone from roughly 300 ppm to roughly 400 ppm. Let's be pessimistic: \Delta T = 0.5 C. Beers-Lambert etc suggest a (natural) logarithmic warming response to atmospheric forcing, so we might expect to see roughly half of the warming in the first third of the increase. Which is (and pay attention, as this is important!) **exactly what is observed**.

So forget non-computable natural variation. Forget assertions of runaway warming due to non-computable presumptions of *positive* feedback from water vapor in a system that is manifestly stable against annual variations in forcing almost 100x greater than the total additional forcing expected upon a doubling of CO_2 -- any sort of sane stability analysis would conclude before even examining the issue in any detail that the mostly likely sign to *any* sort of forcing feedback is *negative*, see remarks above, and more likely than not would *reduce* the observed warming, not increase it, although in a non-computable, nonlinear, chaotic, damped, driven macroscopic system of this sort simple glib assumptions could easily be wrong *in either direction*, which is why we prefer to rely on *what nature tells us* not what we think might be the case a priori. If we admit our ignorance, and ask the simple question: "Do we need to worry about feedbacks increasing the warming that "should" result from doubling CO_2 alone?" the answer is unambiguously * ***No!**

Not from my opinion, not from any real computation, just from a back of the envelope computation **compared to observation**. Well, back of the envelope given the results of any of the many papers estimating or measuring the expected CO_2-only forcing. Indeed, if anything the data suggest that we are surprisingly *close* to this expected rate of total warming over the era where CO_2 has increased by roughly 1/3.

The big question is: why should anybody believe that we *need* additional stuff to explain this variation? And that's attributing 100% of the observed warming to CO_2 only, and using the most optimistic of heavily processed thermometric data "adjusted" over and over again to increase the "instrumental" warming (but curiously, never *decreasing* it, although one would ordinarily expect the probability of errors in measurement to be distributed without bias, at least until one thinks about the obvious UHI *warming* bias that is not removed in the HADCRUT4 data presented in the graph above).

Note that no end points were cherrypicked in this. No trends, linear or nonlinear, were fit. We just take two numbers -- \Delta T and \Delta P_CO_2/P_CO_2 -- and connect them from almost anywhere in the vicinity of 1950 to almost anywhere in the vicinity of the present, and we conclude that the warming observed can be completely explained without invoking any sort of feedback, and without spending a small fortune doing computations that we have no good reason to think have any predictive value at all, that do *not* fit the data particularly well anywhere outside of their reference period, which was (inexplicably!) chosen to be the single stretch of visible warming in the second half of the twentieth century, punctuated by (and probably at least partially caused by!) ENSO events.

So by all means, assert that *since I disagree with the experts* I must be wrong. Assert that *since I said* that the GHE doesn't exist (straw man -- I said nothing of the sort) or that CO_2 isn't part of it (ditto) I must not even have ever looked at a spectrograph even though I explicitly said I did (hmm, it's getting hard to count here -- a bit of ad hominem (basically free, in arguments of this sort) plus assertions of my dishonesty and incompetence devoid of any sort of factual support. To me, it seems that you are perfectly happy to argue using logical fallacy instead of addressing what I say, to the point where I'm tempted indeed to get out a logical fallacy bingo card and see if I've already got a two or three paragraph winner.

Or, you could address the actual points I make, learning about null hypotheses in hypothesis testing (and perhaps Ockham's razor and a few other related principles) along the way if you need to to keep up.

Here's the very simplest picture possible of the point I'm making. Consider a mass on a spring in a damping fluid, being driven not particularly near resonance by a force that consists of two pieces:

F_tot = F_0 + A\cos(\omega t)

where A is roughly 0.07 F_0 (and time is measured in years). Wait for the system to arrive at equilibrium. When it does, it will be oscillating around a displaced equilibrium (displaced by F_0), with an amplitude determined by the need to balance total energy added to the system by A\cos(\omega t) against the total energy removed by the damping force.

Now change one thing: Make F_0 = F_0 + 0.01A, that is, add roughly *one part in a thousand* of F_0 to F_0. *Without* redoing everything, *estimate* the change in the solution. You basically have three choices:

a) The equilibrium shifts by 0.01A/k (where k is the effective spring constant of the oscillator) and nothing else happens.

b) The equilibrium shifts by 0.02A/k to 0.05A/k.

c) The whole system races out of control, with the amplitude varying wildly higher until the spring breaks.

a) is what happens for a linear response model. b) is possible *only* if there are nonlinear terms large enough to *double* (or worse) a linear response to what is a tiny perturbation. Be prepared to carefully justify your Taylor series and prove the existence of the nonlinear terms in the actual trajectory observed before the shift (where the oscillation obviously samples them). c) is what happens if the system is nonlinear and is on the threshold of chaos. Damping, in general, shifts the system *towards linear stability* -- indeed b) is basically asserting highly nonlinear damping (or a highly nonlinear spring) but that sort of damping is *already contradicted* by the observed stability of the oscillator with A approx 0.07 F. If nothing else, it is a lot harder to imagine an integrated response of 2 to 5 times the usual linear response without a most peculiar damping behavior, one that I think is overwhelmingly inconsistent with the data.

To conclude, the *simplest* estimate for the warming expected from doubling CO_2 is 1 C. This estimate is entirely consistent with observations, and is if anything in almost too good agreement with it. There is absolutely no doubt that it is well within any sort of reasonable *error bars*, given that it is near the middle with very little error to be explained even by natural variation and noise. One cannot defend assertions of *catastrophic* climate change by any sort of simplistic argument such as "doubling CO_2 is expected to cause 2 to 5 C warming by 2100" as if this result is somehow *obvious* or *supported by the data*-- it is not. It relies on an entire tower of shaky assumptions and attempts to compute something that is probably not computable (and is definitely not measurable) against noise and natural variation an easy 1-2 orders of magnitude larger. It is inconsistent with experimental observations of *non*-catastrophic warming resulting from doubling CO_2. We are, in fact, dead on the *expected* linear response track, empirically, from 1950 on, and can reasonably expect to see another 0.3 to 0.4 C as we go from 400 ppm CO_2 to 500 ppm CO_2, and the remaining 0.1-0.3 C as we go from 500 ppm to 600 ppm, *if* -- and it is a big if -- natural variations of the same order to do not trump this one way or another, or *net negative* natural feedbacks kick in to further limit the observed warming, or chaos assert itself in the underlying nonlinear chaotic system and kick us into runaway warming or the next glacial episode.

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